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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The Godbillon-Vey invariant of a transversely homogeneous foliation


Authors: Robert Brooks and William Goldman
Journal: Trans. Amer. Math. Soc. 286 (1984), 651-664
MSC: Primary 53C12; Secondary 55R40, 57R32
DOI: https://doi.org/10.1090/S0002-9947-1984-0760978-9
MathSciNet review: 760978
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Abstract: A real projective foliation is a foliation $ \mathfrak{F}$ with a system of local coordinates transverse to $ \mathfrak{F}$ modelled on $ {\mathbf{R}}{P^1}$ (so that the coordinate changes are real linear fractional transformations). Given a closed manifold $ M$, there is but a finite set of values in $ {H^3}(M;{\mathbf{R}})$ which the Godbillon-Vey invariant of such foliations may assume. A bound on the possible values, in terms of the fundamental group, is computed. For $ M$ an oriented circle bundle over a surface, this finite set is explicitly computed.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0760978-9
Article copyright: © Copyright 1984 American Mathematical Society